Perimeter - Examples, Exercises and Solutions

Question Types:
Circumference: Increasing a specific element by addition of.....or multiplication by.......Circumference: Using Pythagoras' theoremCircumference: Verifying whether or not the formula is applicablePerimeter of a Parallelogram: Using the properties of the perimeter of the parallelogramPerimeter of a Triangle: The Perimeter of a TriangleCircumference: Subtraction or addition to a larger shapePerimeter of a Rectangle: Finding Area based off Perimeter and Vice VersaPerimeter of a Triangle: Finding Area based off Perimeter and Vice VersaCircumference: A shape consisting of several shapes (requiring the same formula)Circumference: Using variablesPerimeter of a Rectangle: Applying the formulaCircumference: Calculating parts of the circleCircumference: Identifying and defining elementsPerimeter of a Trapezoid: Finding Area based off Perimeter and Vice VersaCircumference: Using additional geometric shapesPerimeter of a Trapezoid: Using variablesCircumference: Worded problemsPerimeter of a Trapezoid: Comparison between 2 of the same shape with an identical perimeterPerimeter of a Triangle: Applying the formulaPerimeter of a Trapezoid: Calculate The Missing Side based on the formulaPerimeter of a Parallelogram: Using additional geometric shapesPerimeter of a Rectangle: Using congruence and similarityCircumference: Identify the greater valuePerimeter of a Parallelogram: Calculate The Missing Side based on the formulaPerimeter of a Parallelogram: Using variablesPerimeter of a Trapezoid: Applying the formulaPerimeter of a Rectangle: Using Pythagoras' theoremCircumference: Finding Area based off Perimeter and Vice VersaPerimeter of a Rectangle: Comprehension exercisesPerimeter of a Rectangle: Using variablesPerimeter of a Parallelogram: Applying the formulaPerimeter of a Parallelogram: Finding Area based off Perimeter and Vice VersaCircumference: Calculate The Missing Side based on the formulaCircumference: Applying the formula

What is the perimeter?

The perimeter indicates the distance we will walk if we start from a certain point, complete a full lap, and return exactly to the starting point.
For example, if we are asked what the perimeter of the waist is, we will take a tape measure and measure the perimeter from a certain point until completing a full lap and returning to the same point from which we started the measurement.
It works exactly the same way in mathematics. The perimeter of any shape is the distance from a specific point back to it after having completely surrounded it.
If this is our figure:

What is the perimeter

Its perimeter will be the distance we cover if we travel along its line from a certain point, and return to it after making a full lap. Imagine that you are surrounding the figure:

Detailed explanation

Suggested Topics to Practice in Advance

  1. Area
  2. The sides or edges of a triangle
  3. Triangle Height
  4. The Sum of the Interior Angles of a Triangle
  5. Exterior angles of a triangle
  6. Types of Triangles
  7. Obtuse Triangle
  8. Equilateral triangle
  9. Identification of an Isosceles Triangle
  10. Scalene triangle
  11. Acute triangle
  12. Isosceles triangle
  13. The Area of a Triangle
  14. Area of a right triangle
  15. Area of Isosceles Triangles
  16. Area of a Scalene Triangle
  17. Area of Equilateral Triangles

Practice Perimeter

Question 1

Look at the rectangle below.

Side AB is 2 cm long and side BC has a length of 7 cm.

What is the perimeter of the rectangle?
222777AAABBBCCCDDD

Question 2

Look at the rectangle below.

Side AB is 4.8 cm long and side AD has a length of 12 cm.

What is the perimeter of the rectangle?
4.84.84.8121212AAABBBCCCDDD

Question 3

Look at the rectangle below.

Side DC has a length of 1.5 cm and side AD has a length of 9.5 cm.

What is the perimeter of the rectangle?

1.51.51.5AAABBBCCCDDD9.5

Question 4

O is the center of the circle in the figure below.

888OOO What is its circumference?

Question 5

What is the perimeter of the trapezoid in the figure?

444555999666

Examples with solutions for Perimeter

Exercise #1

Look at the rectangle below.

Side AB is 2 cm long and side BC has a length of 7 cm.

What is the perimeter of the rectangle?
222777AAABBBCCCDDD

Video Solution

Step-by-Step Solution

Since in a rectangle every pair of opposite sides are equal to each other, we can claim that:

AB=CD=2 AB=CD=2

AD=BC=7 AD=BC=7

Now we can add all the sides together and find the perimeter:

2+7+2+7=4+14=18 2+7+2+7=4+14=18

Answer

18 cm

Exercise #2

Look at the rectangle below.

Side AB is 4.8 cm long and side AD has a length of 12 cm.

What is the perimeter of the rectangle?
4.84.84.8121212AAABBBCCCDDD

Video Solution

Step-by-Step Solution

In the drawing, we have a rectangle, although it is not placed in its standard form and is slightly rotated,
but this does not affect that it is a rectangle, and it still has all the properties of a rectangle.
 
The perimeter of a rectangle is the sum of all its sides, that is, to find the perimeter of the rectangle we will have to add the lengths of all the sides.
We also know that in a rectangle the opposite sides are equal.
Therefore, we can use the existing sides to complete the missing lengths.
 
4.8+4.8+12+12 =
33.6 cm

Answer

33.6 cm

Exercise #3

Look at the rectangle below.

Side DC has a length of 1.5 cm and side AD has a length of 9.5 cm.

What is the perimeter of the rectangle?

1.51.51.5AAABBBCCCDDD9.5

Video Solution

Step-by-Step Solution

Since in a rectangle every pair of opposite sides are equal to each other, we can claim that:

AD=BC=9.5 AD=BC=9.5

AB=CD=1.5 AB=CD=1.5

Now we can add all the sides together and find the perimeter:

1.5+9.5+1.5+9.5=19+3=22 1.5+9.5+1.5+9.5=19+3=22

Answer

22 cm

Exercise #4

O is the center of the circle in the figure below.

888OOO What is its circumference?

Video Solution

Step-by-Step Solution

We use the formula:P=2πr P=2\pi r

We replace the data in the formula:P=2×8π P=2\times8\pi

P=16π P=16\pi

Answer

16π 16\pi cm

Exercise #5

What is the perimeter of the trapezoid in the figure?

444555999666

Video Solution

Step-by-Step Solution

To find the perimeter we will add all the sides:

4+5+9+6=9+9+6=18+6=24 4+5+9+6=9+9+6=18+6=24

Answer

24

Question 1

Look at the triangle below:

666888101010

What is the perimeter of the triangle?

Question 2

Given the triangle:

777111111131313

What is its perimeter?

Question 3

Look at the trapezoid in the diagram.

101010777121212777

What is its perimeter?

Question 4

Look at the circle in the figure:

444

Its radius is equal to 4.

What is its circumference?

Question 5

Look at the following rectangle:

AAABBBCCCDDD95

Find its perimeter.

Exercise #6

Look at the triangle below:

666888101010

What is the perimeter of the triangle?

Video Solution

Step-by-Step Solution

The perimeter of the triangle is equal to the sum of all sides together, therefore:

6+8+10=14+10=24 6+8+10=14+10=24

Answer

24

Exercise #7

Given the triangle:

777111111131313

What is its perimeter?

Video Solution

Step-by-Step Solution

The perimeter of a triangle is equal to the sum of all its sides together:

11+7+13=11+20=31 11+7+13=11+20=31

Answer

31

Exercise #8

Look at the trapezoid in the diagram.

101010777121212777

What is its perimeter?

Video Solution

Step-by-Step Solution

In order to calculate the perimeter of the trapezoid we must add together the measurements of all of its sides:

7+10+7+12 =

36

And that's the solution!

Answer

36

Exercise #9

Look at the circle in the figure:

444

Its radius is equal to 4.

What is its circumference?

Video Solution

Step-by-Step Solution

The formula for the circumference is equal to:

2πr 2\pi r

Answer

8π

Exercise #10

Look at the following rectangle:

AAABBBCCCDDD95

Find its perimeter.

Video Solution

Step-by-Step Solution

Since in a rectangle all pairs of opposite sides are equal:

AD=BC=5 AD=BC=5

AB=CD=9 AB=CD=9

Now we calculate the perimeter of the rectangle by adding the sides:

5+5+9+9=10+18=28 5+5+9+9=10+18=28

Answer

28

Question 1

Look at the rectangle below:

AAABBBCCCDDD107

Calculate its perimeter.

Question 2

666444AAABBBDDDCCC

Calculate the perimeter of the given parallelogram:

Question 3

101010777AAABBBDDDCCC

Calculate the perimeter of the given parallelogram.

Question 4

Look at the circle in the figure.

What is its circumference if its radius is equal to 6?

6

Question 5

Calculate the perimeter of the parallelogram ABCD.

CD is parallel to AB.

777121212AAABBBCCCDDD

Exercise #11

Look at the rectangle below:

AAABBBCCCDDD107

Calculate its perimeter.

Video Solution

Step-by-Step Solution

Since in a rectangle every pair of opposite sides are equal to each other, we can claim that:

AB=CD=10 AB=CD=10

BC=AD=7 BC=AD=7

Now let's add all the sides together to find the perimeter of the rectangle:

10+7+10+7=20+14=34 10+7+10+7=20+14=34

Answer

34

Exercise #12

666444AAABBBDDDCCC

Calculate the perimeter of the given parallelogram:

Video Solution

Step-by-Step Solution

As is true for a parallelogram every pair of opposite sides are equal:

AB=CD=6,AC=BD=4 AB=CD=6,AC=BD=4

The perimeter of the parallelogram is equal to the sum of all sides together:

4+4+6+6=8+12=20 4+4+6+6=8+12=20

Answer

20

Exercise #13

101010777AAABBBDDDCCC

Calculate the perimeter of the given parallelogram.

Video Solution

Step-by-Step Solution

As is true for a parallelogram each pair of opposite sides are equal and parallel,

Therefore it is possible to argue that:

AC=BD=7 AC=BD=7

AB=CD=10 AB=CD=10

Now we can calculate the perimeter of the parallelogram by adding together all of its sides:

10+10+7+7=20+14=34 10+10+7+7=20+14=34

Answer

34

Exercise #14

Look at the circle in the figure.

What is its circumference if its radius is equal to 6?

6

Video Solution

Step-by-Step Solution

Formula of the circumference:

P=2πr P=2\pi r

We insert the given data into the formula:

P=2×6×π P=2\times6\times\pi

P=12π P=12\pi

Answer

12π 12\pi

Exercise #15

Calculate the perimeter of the parallelogram ABCD.

CD is parallel to AB.

777121212AAABBBCCCDDD

Video Solution

Step-by-Step Solution

Let's recall the properties of parallelograms, where pairs of opposite sides are parallel and equal.

Therefore, AB is parallel to CD

Therefore, BC is parallel to AD

From this, we can conclude that AB=CD=7

And also BC=AD=12

Now we can calculate the perimeter by adding all the sides together:

7+7+12+12=14+24=38 7+7+12+12=14+24=38

Answer

38

Topics learned in later sections

  1. Triangle
  2. Perimeter of a triangle